Blender does not create direct associations between Actions / Slots and the objects with which they were originally created or are compatible, and delegates this bound to direct linking between an object and a single action through its animation data, or to coordination in the NLA.
Action Binder creates Animation Groups, which associates an Action with Slots to Objects / Data, allowing you to quickly switch between complex animations with multiple entities involved, and easily export them in FBX format.
Several Animations can be created using the same actions but binding different objects to it.
View3D > Sidebar > Animations
- Removes any linked animation data, resets the bone positions, shape keys and custom attributes to default values, of the selected objects.
Pushes every Animation group actions to their corresponding object tracks in the NLA sequentially.
Creates a new Action from all the currently selected objects, including object transforms, poses and shapekeys values.
Creates a new Animation Group per Action, binding the the most probable object into each slot automatically. If an action is already bound to another Animation Group it will not create a new one.
I have created a modified version of Unity's FBX exporter that allows you to export Animation Groups as individual FBXAnimStacks. You can download FBX Plus here.